We wish to understand the principles governing the three-dimensional (3D) architecture of biological RNAs and their mechanisms of action. RNAs and proteins are unique among biological macromolecules in being able to self-organize to adopt 3D conformations that are specified by their sequences. It is their 3D structures that enables these macromolecules to carry out the biochemical transformations that underlie all of cell biology. Whereas hundreds of protein structures have been determined at high resolution, the detailed 3D structures of only a handful of biologically-functional RNAs are known. We wish to understand, in atomic detail, how RNAs can fold into compact 3D structures with solvent-inaccessible interiors, how they can catalyze biochemical transformations and how RNA structure is exploited for specific RNA-protein interactions. We study two classes of model systems: catalytic RNAs (ribozymes), and protein enzymes responsible for post-transcriptional RNA modifications. We study the hairpin ribozyme and the Varkud satellite (VS) ribozyme. These two naturally-occurring ribozymes catalyze the same overall chemical transformation, yet appear to have unrelated 3D structures and to use different catalytic mechanisms. We study pseudouridine (psi) synthases, a family of protein enzymes responsible for the most abundant type of post- transcriptional modification of cellular RNAs. These enzymes must modify only specific residues of their substrate RNAs, and have evolved sophisticated means of recognizing the structures of their substrates. Our experimental approach combines X-ray crystallography and biochemistry. We will visualize the ground- state structures of our model macromolecules at atomic or near- atomic resolution by crystallography. The structures will suggest hypotheses about the mechanisms of action of these macromolecules in terms of specific atomic groups and their interactions. These hypotheses will be tested by modifying the candidate atomic groups by either site-directed mutagenesis or synthetic chemistry. The latter is feasible with extant methodology since our model systems are of relatively modest size (less than 50 kDa). Because our model systems are all catalysts, we can then employ the sensitive tools of enzyme kinetics to read out the effects of our targeted perturbations on the activity of the macromolecules. We will also analyze how the structure of our model RNAs changes during the act of catalysis. We will employ the tools of time-resolved crystallography to accomplish this. Finally, we will employ biochemistry and crystallography to analyze how, in eukaryotes, certain nucleolar RNAs scaffold the assembly of psi synthases and accessory proteins into versatile catalytic machines.